Abstract

Ridge and valley enhancing filters are widely used in applications such as vessel detection in medical image computing. When images are degraded by noise or include vessels at different scales, such filters are an essential step for meaningful and stable vessel localization. In this work, we propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a fourth-order diffusion tensor whose eigentensors and eigenvalues are determined from the local Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient implementation using a fast explicit diffusion scheme and demonstrate results on synthetic images and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters, as well as established second-order vessel enhancing filters, our newly proposed one better restores the centerlines in all cases.

Bilder

Zusätzliches Material

Bibtex

@ARTICLE{GorgiZadeh:JMIV17,
author = {Gorgi Zadeh, Shekoufeh and Didas, Stephan and Wintergerst, Maximilian and Schultz, Thomas},
title = {Multi-scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization},
journal = {Journal of Mathematical Imaging and Vision},
year = {2017},
note = {First online April 11, 2017},
abstract = {Ridge and valley enhancing filters are widely used in applications such as vessel detection in
medical image computing. When images are degraded by noise or include vessels at different scales,
such filters are an essential step for meaningful and stable vessel localization. In this work, we
propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth
along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a
fourth-order diffusion tensor whose eigentensors and eigenvalues are determined from the local
Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient
implementation using a fast explicit diffusion scheme and demonstrate results on synthetic images
and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters,
as well as established second-order vessel enhancing filters, our newly proposed one better restores
the centerlines in all cases.},
doi = {10.1007/s10851-017-0729-1}
}